From the Archives highlights articles from NCTM’s legacy journals, as chosen by leaders in mathematics education.

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### Catherine A. Little, Sherryl Hauser, Jeffrey Corbishley, and Introduction by: Denise M. Walston

### Jerilynn Lepak and Taren Going

Teaching transparently about the process and goals can support students as they make and support mathematical claims.

### Patrick Sullivan

Draw on two simulations to introduce compound events and help your class make connections between experimental and theoretical probabilities.

### Jessica Pierson Bishop, Lisa L. Lamb, Ian Whitacre, Randolph A. Philipp, and Bonnie P. Schappelle

Are your students negative about integers? Help them experience positivity and joy doing integer arithmetic!

### Hyunyi Jung, Ji-Won Son, and Ji-Yeong I

Use a COVID-19 lesson as an example of how to apply a framework aligned with research recommendations to support students as they apply mathematics to real life.

### Kate Degner

Using question 28 from the May Problems to Ponder in volume 114, the author and her seventh- and eighth-grade students launched into a discussion of creativity, linearity, piecewise, and recursive definitions of functions. This pattern to ponder provided rich mathematical opportunities for all students in my middle school classroom.

### Dorothy Y. White

Use this activity to support students in working together, recognizing one another’s contributions, and leveraging their mathematical strengths to solve challenging problems.

### Hyunyi Jung, Megan H. Wickstrom, and Chris Piasecki

The Great Pacific Garbage Patch activity involves an urgent environmental issue that students can discuss. It engages students in the interpretation of visual data, measurements, units, and the area of regular and irregular figures.

### Jeff Gregg, Diana Underwood Gregg, and Introduction by: Melissa Boston

From the Archives highlights articles from NCTM’s legacy journals, as chosen by leaders in mathematics education.

### Courtney K. Baker, Terrie M. Galanti, Kimberly Morrow-Leong, and Tammy Kraft

The Teaching for Robust Understanding framework facilitates online collaborative problem solving with digital interactive notebooks that position all students as doers of mathematics.